I say go with LBP 2. Everything LBP 1 did, LBP 2 greatly improves on it. You can access all the user-made levels from LBP 1 on LBP 2 and it has a much nicer campaign. Your daughter won't be missing anything by skipping the first one.

My son (almost 7yrs old) has not touched Little Big Planet since we purchased LBP2. Part 2 imported the sack people that he created from part 1 which was kinda cool, but I'm not sure if it works conversely. Nor do I know if my kid would be into part one if we had purchased part 2 first (although I suspect he would.)

If you can get LBP2 for free, I say go for it. It's loads of fun with lots of replay value. Although I can't see either of these two titles winding up in a game shop's "used bin" any time soon, the possibility of either of these titles being re-released as "greatest hits" title is likely. Part one would probably be a little cheaper if that were to happen as it is older, making LBP2 a better choice for a free game in the meantime, imo.